Physiologic organs consist of various types of cells organized into tissues. These tissues form an organ, which in turn interacts with the whole body. The ability to model organ function with a high level of biophysical, biochemical, and structural detail is of enormous value to biology and medicine, because such models provide deep insight into the cause of disease.
Given the immense complexity of even the simplest organ, the principal task that confronts the model builder is to recognize what biophysical detail can be successfully disregarded in constructing a computationally useful model.
The heart for example includes a sino-atrial node and atrio-ventricular node, as well as the bundle of His and the Purkinje fiber system. These structures have a profound impact on the electrical activation sequence of the heart muscle fibers within the atria and ventricles, and thus have an enormous impact on the heart's mechanical function. It is well known that organic and anatomic defects in these structures can result in life-threatening cardiac arrhythmias. A model that allows a user to interact with an accurate and predictive model of the heart's cells and tissues would be of great value.
This objective has spurred the development of computational models of cardiac cells and tissues. These computational models have sought to integrate experimental observations and theoretical knowledge into a formal model expressed in mathematical terms. Various algorithms, processes and procedures are used to describe the behavior of the cells and tissues that comprise the organ system. A useful computer-implemented model should effectively emulate interesting behaviors.
The earliest mathematical models of the heart used formal mathematical assumptions about cellular physiology; for example Van der Pol and Mark's description of the heartbeat as a relaxation oscillator in 1928. Real physiological parameters were not included in models until 1952 when Hodgkin and Huxley explained their observations on the action potential of the giant squid axon in their classic work on membrane processes and ion fluxes. The success of their work can be measured by the many models that have followed their paradigm to model systems as diverse as neurons, cardiac cells, pancreatic beta cells, and other excitable cells. One descendent model was the 1962 Noble model of the cardiac Purkinje fiber which was based on experimental evidence that two potassium conductances, together with a sodium conductance, are sufficient to generate action potentials and pacemaker potentials.
Technical innovations have led to more precise experimental data which in turn has led to the ongoing refinement of models as new information has been incorporated. The result has been that the accuracy and predictability of models have been upgraded with respect to actual biophysical and physiological parameters; for example, beginning with the Noble model of the Purkinje fiber, subsequent experiments extended the description of cardiac electrophysiology to include more refined models of the Purkinje conducting system, as well as sinus node, atrial, and ventricular cells. These single cell models have evolved, through successive improvements and refinements, into a software package called "OXSOFT HEART 4.5" presently available to investigators under license from Takhus, Inc.
Presently the "OXSOFT" model is restricted to the modeling of cardiac function at the single cell (or "zero-dimensional") level. This model incorporates mathematical expressions that represent the biochemical, biophysical, and cellular mechanisms (Hodgkin-Huxley) within single cardiac cells. These equations collectively define a given cardiac-cell state.
The "OXSOFT" models require the solution of thirty or more simultaneous non-linear differential equations. Even on the fastest personal computers it can take several minutes to compute only a few seconds of activity. Nonetheless zero-dimensional models have proven to be successful not only in reproducing normal single cell cardiac electrical activity, but also in reconstructing some of the cellular mechanisms of arrhythmia, including ectopic beating and the effects of therapeutic drug administration (e.g., cardiac glycosides). These models can exhibit the action potential shortening during ATP depletion, and the early after-depolarizations characteristic of potassium blocking compounds and calcium agonists observed in actual hearts. Initial success has prompted researchers to try to extend the dimensionally of these models but just how best to do this has remained elusive.
To date, efforts to extend the single cell models and to develop large scale higher dimensional models usually have favored simplicity, flexibility, and computational efficiency. While these characteristics make it possible to simulate large systems for extended periods, it requires that biophysical and biochemical mechanisms essential to the explanation of arrhythmias be extrapolated and rule driven. Extrapolation of the essential mechanisms governing real systems is done by guesswork and, to some extent is justified only when basic rules have been tested in simulation. Such models are not usefully predictive.
Some limitations of existing 1-D and 2-D models have been eliminated by development of a software packages called "SA" and "VENT", licensed to Physiome Sciences Inc. These one- and two-dimensional network models of the mammalian sino-atrial node, atrium, and ventricles incorporate all of the biophysical detail described within the "OXSOFT" single cell models, but also account for cell to cell propagation of electrical activity within simple cardiac cell networks. When 1-D and 2-D models are iterated by the computer, the state of the various nodes change, giving rise to data that expresses the propagation of electric wave fronts in the model. However the 2-D model's electrophysiological wave front characteristics do not accurately mimic the complex characteristics of actual arrhythmias.
Many laboratories value this work but existing versions of Oxsoft HEART, AS, and VENT (1-D and 2-D network models) neither simulate nor accurately predict the heart's three-dimensional electrophysiological behavior.